/*
-----------------------------------------------------------------------------
This source file is part of OGRE
(Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2009 Torus Knot Software Ltd

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
-----------------------------------------------------------------------------
*/
#include <limits>
#include "BasicMath.h"
#include "Vector3.h"
#include "Vector2.h"
#include "Plane.h"
#include "Ray.h"
#include "AxisAlignedBox.h"
#  pragma warning (push)
#  pragma warning (disable : 4305)


const float Math::POS_INFINITY = std::numeric_limits<float>::infinity();
const float Math::NEG_INFINITY = -std::numeric_limits<float>::infinity();
const float Math::PI = float( 4.0 * atan( 1.0 ) );
const float Math::TWO_PI = float( 2.0 * PI );
const float Math::HALF_PI = float( 0.5 * PI );
const float Math::fDeg2Rad = PI / float(180.0);
const float Math::fRad2Deg = float(180.0) / PI;
const float Math::LOG2 = log(float(2.0));

int Math::mTrigTableSize;
Math::AngleUnit Math::msAngleUnit;

float  Math::mTrigTableFactor;
float *Math::mSinTable = NULL;
float *Math::mTanTable = NULL;

//-----------------------------------------------------------------------
Math::Math( unsigned int trigTableSize )
{
	msAngleUnit = AU_DEGREE;

	mTrigTableSize = trigTableSize;
	mTrigTableFactor = mTrigTableSize / Math::TWO_PI;

	mSinTable = new float[mTrigTableSize];
	mTanTable = new float[mTrigTableSize];

	buildTrigTables();
}

//-----------------------------------------------------------------------
Math::~Math()
{
	delete[] mSinTable;
	delete[] mTanTable;
}

//-----------------------------------------------------------------------
void Math::buildTrigTables(void)
{
	// Build trig lookup tables
	// Could get away with building only PI sized Sin table but simpler this 
	// way. Who cares, it'll ony use an extra 8k of memory anyway and I like 
	// simplicity.
	float angle;
	for (int i = 0; i < mTrigTableSize; ++i)
	{
		angle = Math::TWO_PI * i / mTrigTableSize;
		mSinTable[i] = sin(angle);
		mTanTable[i] = tan(angle);
	}
}
//-----------------------------------------------------------------------	
float Math::SinTable (float fValue)
{
	// Convert range to index values, wrap if required
	int idx;
	if (fValue >= 0)
	{
		idx = int(fValue * mTrigTableFactor) % mTrigTableSize;
	}
	else
	{
		idx = mTrigTableSize - (int(-fValue * mTrigTableFactor) % mTrigTableSize) - 1;
	}

	return mSinTable[idx];
}
//-----------------------------------------------------------------------
float Math::TanTable (float fValue)
{
	// Convert range to index values, wrap if required
	int idx = int(fValue *= mTrigTableFactor) % mTrigTableSize;
	return mTanTable[idx];
}
//-----------------------------------------------------------------------
int Math::ISign (int iValue)
{
	return ( iValue > 0 ? +1 : ( iValue < 0 ? -1 : 0 ) );
}
//-----------------------------------------------------------------------
Radian Math::ACos (float fValue)
{
	if ( -1.0 < fValue )
	{
		if ( fValue < 1.0 )
			return Radian(acos(fValue));
		else
			return Radian(0.0);
	}
	else
	{
		return Radian(PI);
	}
}
//-----------------------------------------------------------------------
Radian Math::ASin (float fValue)
{
	if ( -1.0 < fValue )
	{
		if ( fValue < 1.0 )
			return Radian(asin(fValue));
		else
			return Radian(HALF_PI);
	}
	else
	{
		return Radian(-HALF_PI);
	}
}
//-----------------------------------------------------------------------
float Math::Sign (float fValue)
{
	if ( fValue > 0.0 )
		return 1.0;

	if ( fValue < 0.0 )
		return -1.0;

	return 0.0;
}
//-----------------------------------------------------------------------
float Math::UnitRandom ()
{
	return (float)rand() / RAND_MAX;
}

//-----------------------------------------------------------------------
float Math::RangeRandom (float fLow, float fHigh)
{
	return (fHigh-fLow)*UnitRandom() + fLow;
}

//-----------------------------------------------------------------------
float Math::SymmetricRandom ()
{
	return 2.0f * UnitRandom() - 1.0f;
}

//-----------------------------------------------------------------------
void Math::setAngleUnit(Math::AngleUnit unit)
{
	msAngleUnit = unit;
}
//-----------------------------------------------------------------------
Math::AngleUnit Math::getAngleUnit(void)
{
	return msAngleUnit;
}
//-----------------------------------------------------------------------
float Math::AngleUnitsToRadians(float angleunits)
{
	if (msAngleUnit == AU_DEGREE)
		return angleunits * fDeg2Rad;
	else
		return angleunits;
}

//-----------------------------------------------------------------------
float Math::RadiansToAngleUnits(float radians)
{
	if (msAngleUnit == AU_DEGREE)
		return radians * fRad2Deg;
	else
		return radians;
}

//-----------------------------------------------------------------------
float Math::AngleUnitsToDegrees(float angleunits)
{
	if (msAngleUnit == AU_RADIAN)
		return angleunits * fRad2Deg;
	else
		return angleunits;
}

//-----------------------------------------------------------------------
float Math::DegreesToAngleUnits(float degrees)
{
	if (msAngleUnit == AU_RADIAN)
		return degrees * fDeg2Rad;
	else
		return degrees;
}

//-----------------------------------------------------------------------
bool Math::pointInTri2D(const Vector2& p, const Vector2& a, 
	const Vector2& b, const Vector2& c)
{
	// Winding must be consistent from all edges for point to be inside
	Vector2 v1, v2;
	float dot[3];
	bool zeroDot[3];

	v1 = b - a;
	v2 = p - a;

	// Note we don't care about normalisation here since sign is all we need
	// It means we don't have to worry about magnitude of cross products either
	dot[0] = v1.crossProduct(v2);
	zeroDot[0] = Math::RealEqual(dot[0], 0.0f, 1e-3);


	v1 = c - b;
	v2 = p - b;

	dot[1] = v1.crossProduct(v2);
	zeroDot[1] = Math::RealEqual(dot[1], 0.0f, 1e-3);

	// Compare signs (ignore colinear / coincident points)
	if(!zeroDot[0] && !zeroDot[1] 
	&& Math::Sign(dot[0]) != Math::Sign(dot[1]))
	{
		return false;
	}

	v1 = a - c;
	v2 = p - c;

	dot[2] = v1.crossProduct(v2);
	zeroDot[2] = Math::RealEqual(dot[2], 0.0f, 1e-3);
	// Compare signs (ignore colinear / coincident points)
	if((!zeroDot[0] && !zeroDot[2] 
	&& Math::Sign(dot[0]) != Math::Sign(dot[2])) ||
		(!zeroDot[1] && !zeroDot[2] 
	&& Math::Sign(dot[1]) != Math::Sign(dot[2])))
	{
		return false;
	}


	return true;
}
//-----------------------------------------------------------------------
bool Math::pointInTri3D(const Vector3& p, const Vector3& a, 
	const Vector3& b, const Vector3& c, const Vector3& normal)
{
	// Winding must be consistent from all edges for point to be inside
	Vector3 v1, v2;
	float dot[3];
	bool zeroDot[3];

	v1 = b - a;
	v2 = p - a;

	// Note we don't care about normalisation here since sign is all we need
	// It means we don't have to worry about magnitude of cross products either
	dot[0] = v1.crossProduct(v2).dotProduct(normal);
	zeroDot[0] = Math::RealEqual(dot[0], 0.0f, 1e-3);


	v1 = c - b;
	v2 = p - b;

	dot[1] = v1.crossProduct(v2).dotProduct(normal);
	zeroDot[1] = Math::RealEqual(dot[1], 0.0f, 1e-3);

	// Compare signs (ignore colinear / coincident points)
	if(!zeroDot[0] && !zeroDot[1] 
	&& Math::Sign(dot[0]) != Math::Sign(dot[1]))
	{
		return false;
	}

	v1 = a - c;
	v2 = p - c;

	dot[2] = v1.crossProduct(v2).dotProduct(normal);
	zeroDot[2] = Math::RealEqual(dot[2], 0.0f, 1e-3);
	// Compare signs (ignore colinear / coincident points)
	if((!zeroDot[0] && !zeroDot[2] 
	&& Math::Sign(dot[0]) != Math::Sign(dot[2])) ||
		(!zeroDot[1] && !zeroDot[2] 
	&& Math::Sign(dot[1]) != Math::Sign(dot[2])))
	{
		return false;
	}


	return true;
}
//-----------------------------------------------------------------------
bool Math::RealEqual( float a, float b, float tolerance )
{
	if (fabs(b-a) <= tolerance)
		return true;
	else
		return false;
}

//-----------------------------------------------------------------------
std::pair<bool, float> Math::intersects(const Ray& ray, const Plane& plane)
{

	float denom = plane.normal.dotProduct(ray.getDirection());
	if (Math::Abs(denom) < std::numeric_limits<float>::epsilon())
	{
		// Parallel
		return std::pair<bool, float>(false, 0);
	}
	else
	{
		float nom = plane.normal.dotProduct(ray.getOrigin()) + plane.d;
		float t = -(nom/denom);
		return std::pair<bool, float>(t >= 0, t);
	}

}
//-----------------------------------------------------------------------
std::pair<bool, float> Math::intersects(const Ray& ray, 
	const std::vector<Plane>& planes, bool normalIsOutside)
{
	std::list<Plane> planesList;
	for (std::vector<Plane>::const_iterator i = planes.begin(); i != planes.end(); ++i)
	{
		planesList.push_back(*i);
	}
	return intersects(ray, planesList, normalIsOutside);
}
//-----------------------------------------------------------------------
std::pair<bool, float> Math::intersects(const Ray& ray, 
	const std::list<Plane>& planes, bool normalIsOutside)
{
	std::list<Plane>::const_iterator planeit, planeitend;
	planeitend = planes.end();
	bool allInside = true;
	std::pair<bool, float> ret;
	std::pair<bool, float> end;
	ret.first = false;
	ret.second = 0.0f;
	end.first = false;
	end.second = 0;


	// derive side
	// NB we don't pass directly since that would require Plane::Side in 
	// interface, which results in recursive includes since Math is so fundamental
	Plane::Side outside = normalIsOutside ? Plane::POSITIVE_SIDE : Plane::NEGATIVE_SIDE;

	for (planeit = planes.begin(); planeit != planeitend; ++planeit)
	{
		const Plane& plane = *planeit;
		// is origin outside?
		if (plane.getSide(ray.getOrigin()) == outside)
		{
			allInside = false;
			// Test single plane
			std::pair<bool, float> planeRes = 
				ray.intersects(plane);
			if (planeRes.first)
			{
				// Ok, we intersected
				ret.first = true;
				// Use the most distant result since convex volume
				ret.second = std::max(ret.second, planeRes.second);
			}
			else
			{
				ret.first =false;
				ret.second=0.0f;
				return ret;
			}
		}
		else
		{
			std::pair<bool, float> planeRes = 
				ray.intersects(plane);
			if (planeRes.first)
			{
				if( !end.first )
				{
					end.first = true;
					end.second = planeRes.second;
				}
				else
				{
					end.second = std::min( planeRes.second, end.second );
				}

			}

		}
	}

	if (allInside)
	{
		// Intersecting at 0 distance since inside the volume!
		ret.first = true;
		ret.second = 0.0f;
		return ret;
	}

	if( end.first )
	{
		if( end.second < ret.second )
		{
			ret.first = false;
			return ret;
		}
	}
	return ret;
}
//-----------------------------------------------------------------------
std::pair<bool, float> Math::intersects(const Ray& ray, const Sphere& sphere, 
	bool discardInside)
{
	const Vector3& raydir = ray.getDirection();
	// Adjust ray origin relative to sphere center
	const Vector3& rayorig = ray.getOrigin() - sphere.getCenter();
	float radius = sphere.getRadius();

	// Check origin inside first
	if (rayorig.squaredLength() <= radius*radius && discardInside)
	{
		return std::pair<bool, float>(true, 0);
	}

	// Mmm, quadratics
	// Build coeffs which can be used with std quadratic solver
	// ie t = (-b +/- sqrt(b*b + 4ac)) / 2a
	float a = raydir.dotProduct(raydir);
	float b = 2 * rayorig.dotProduct(raydir);
	float c = rayorig.dotProduct(rayorig) - radius*radius;

	// Calc determinant
	float d = (b*b) - (4 * a * c);
	if (d < 0)
	{
		// No intersection
		return std::pair<bool, float>(false, 0);
	}
	else
	{
		// BTW, if d=0 there is one intersection, if d > 0 there are 2
		// But we only want the closest one, so that's ok, just use the 
		// '-' version of the solver
		float t = ( -b - Math::Sqrt(d) ) / (2 * a);
		if (t < 0)
			t = ( -b + Math::Sqrt(d) ) / (2 * a);
		return std::pair<bool, float>(true, t);
	}


}
//-----------------------------------------------------------------------
std::pair<bool, float> Math::intersects(const Ray& ray, const AxisAlignedBox& box)
{
	if (box.isNull()) return std::pair<bool, float>(false, 0);
	if (box.isInfinite()) return std::pair<bool, float>(true, 0);

	float lowt = 0.0f;
	float t;
	bool hit = false;
	Vector3 hitpoint;
	const Vector3& min = box.getMinimum();
	const Vector3& max = box.getMaximum();
	const Vector3& rayorig = ray.getOrigin();
	const Vector3& raydir = ray.getDirection();

	// Check origin inside first
	if ( rayorig > min && rayorig < max )
	{
		return std::pair<bool, float>(true, 0);
	}

	// Check each face in turn, only check closest 3
	// Min x
	if (rayorig.x <= min.x && raydir.x > 0)
	{
		t = (min.x - rayorig.x) / raydir.x;
		if (t >= 0)
		{
			// Substitute t back into ray and check bounds and dist
			hitpoint = rayorig + raydir * t;
			if (hitpoint.y >= min.y && hitpoint.y <= max.y &&
				hitpoint.z >= min.z && hitpoint.z <= max.z &&
				(!hit || t < lowt))
			{
				hit = true;
				lowt = t;
			}
		}
	}
	// Max x
	if (rayorig.x >= max.x && raydir.x < 0)
	{
		t = (max.x - rayorig.x) / raydir.x;
		if (t >= 0)
		{
			// Substitute t back into ray and check bounds and dist
			hitpoint = rayorig + raydir * t;
			if (hitpoint.y >= min.y && hitpoint.y <= max.y &&
				hitpoint.z >= min.z && hitpoint.z <= max.z &&
				(!hit || t < lowt))
			{
				hit = true;
				lowt = t;
			}
		}
	}
	// Min y
	if (rayorig.y <= min.y && raydir.y > 0)
	{
		t = (min.y - rayorig.y) / raydir.y;
		if (t >= 0)
		{
			// Substitute t back into ray and check bounds and dist
			hitpoint = rayorig + raydir * t;
			if (hitpoint.x >= min.x && hitpoint.x <= max.x &&
				hitpoint.z >= min.z && hitpoint.z <= max.z &&
				(!hit || t < lowt))
			{
				hit = true;
				lowt = t;
			}
		}
	}
	// Max y
	if (rayorig.y >= max.y && raydir.y < 0)
	{
		t = (max.y - rayorig.y) / raydir.y;
		if (t >= 0)
		{
			// Substitute t back into ray and check bounds and dist
			hitpoint = rayorig + raydir * t;
			if (hitpoint.x >= min.x && hitpoint.x <= max.x &&
				hitpoint.z >= min.z && hitpoint.z <= max.z &&
				(!hit || t < lowt))
			{
				hit = true;
				lowt = t;
			}
		}
	}
	// Min z
	if (rayorig.z <= min.z && raydir.z > 0)
	{
		t = (min.z - rayorig.z) / raydir.z;
		if (t >= 0)
		{
			// Substitute t back into ray and check bounds and dist
			hitpoint = rayorig + raydir * t;
			if (hitpoint.x >= min.x && hitpoint.x <= max.x &&
				hitpoint.y >= min.y && hitpoint.y <= max.y &&
				(!hit || t < lowt))
			{
				hit = true;
				lowt = t;
			}
		}
	}
	// Max z
	if (rayorig.z >= max.z && raydir.z < 0)
	{
		t = (max.z - rayorig.z) / raydir.z;
		if (t >= 0)
		{
			// Substitute t back into ray and check bounds and dist
			hitpoint = rayorig + raydir * t;
			if (hitpoint.x >= min.x && hitpoint.x <= max.x &&
				hitpoint.y >= min.y && hitpoint.y <= max.y &&
				(!hit || t < lowt))
			{
				hit = true;
				lowt = t;
			}
		}
	}

	return std::pair<bool, float>(hit, lowt);

} 
//-----------------------------------------------------------------------
bool Math::intersects(const Ray& ray, const AxisAlignedBox& box,
	float* d1, float* d2)
{
	if (box.isNull())
		return false;

	if (box.isInfinite())
	{
		if (d1) *d1 = 0;
		if (d2) *d2 = Math::POS_INFINITY;
		return true;
	}

	const Vector3& min = box.getMinimum();
	const Vector3& max = box.getMaximum();
	const Vector3& rayorig = ray.getOrigin();
	const Vector3& raydir = ray.getDirection();

	Vector3 absDir;
	absDir[0] = Math::Abs(raydir[0]);
	absDir[1] = Math::Abs(raydir[1]);
	absDir[2] = Math::Abs(raydir[2]);

	// Sort the axis, ensure check minimise floating error axis first
	int imax = 0, imid = 1, imin = 2;
	if (absDir[0] < absDir[2])
	{
		imax = 2;
		imin = 0;
	}
	if (absDir[1] < absDir[imin])
	{
		imid = imin;
		imin = 1;
	}
	else if (absDir[1] > absDir[imax])
	{
		imid = imax;
		imax = 1;
	}

	float start = 0, end = Math::POS_INFINITY;

#define _CALC_AXIS(i)                                       \
	do {                                                    \
	float denom = 1 / raydir[i];                         \
	float newstart = (min[i] - rayorig[i]) * denom;      \
	float newend = (max[i] - rayorig[i]) * denom;        \
	if (newstart > newend) std::swap(newstart, newend); \
	if (newstart > end || newend < start) return false; \
	if (newstart > start) start = newstart;             \
	if (newend < end) end = newend;                     \
	} while(0)

	// Check each axis in turn

	_CALC_AXIS(imax);

	if (absDir[imid] < std::numeric_limits<float>::epsilon())
	{
		// Parallel with middle and minimise axis, check bounds only
		if (rayorig[imid] < min[imid] || rayorig[imid] > max[imid] ||
			rayorig[imin] < min[imin] || rayorig[imin] > max[imin])
			return false;
	}
	else
	{
		_CALC_AXIS(imid);

		if (absDir[imin] < std::numeric_limits<float>::epsilon())
		{
			// Parallel with minimise axis, check bounds only
			if (rayorig[imin] < min[imin] || rayorig[imin] > max[imin])
				return false;
		}
		else
		{
			_CALC_AXIS(imin);
		}
	}
#undef _CALC_AXIS

	if (d1) *d1 = start;
	if (d2) *d2 = end;

	return true;
}
//-----------------------------------------------------------------------
std::pair<bool, float> Math::intersects(const Ray& ray, const Vector3& a,
	const Vector3& b, const Vector3& c, const Vector3& normal,
	bool positiveSide, bool negativeSide)
{
	//
	// Calculate intersection with plane.
	//
	float t;
	{
		float denom = normal.dotProduct(ray.getDirection());

		// Check intersect side
		if (denom > + std::numeric_limits<float>::epsilon())
		{
			if (!negativeSide)
				return std::pair<bool, float>(false, 0);
		}
		else if (denom < - std::numeric_limits<float>::epsilon())
		{
			if (!positiveSide)
				return std::pair<bool, float>(false, 0);
		}
		else
		{
			// Parallel or triangle area is close to zero when
			// the plane normal not normalised.
			return std::pair<bool, float>(false, 0);
		}

		t = normal.dotProduct(a - ray.getOrigin()) / denom;

		if (t < 0)
		{
			// Intersection is behind origin
			return std::pair<bool, float>(false, 0);
		}
	}

	//
	// Calculate the largest area projection plane in X, Y or Z.
	//
	size_t i0, i1;
	{
		float n0 = Math::Abs(normal[0]);
		float n1 = Math::Abs(normal[1]);
		float n2 = Math::Abs(normal[2]);

		i0 = 1; i1 = 2;
		if (n1 > n2)
		{
			if (n1 > n0) i0 = 0;
		}
		else
		{
			if (n2 > n0) i1 = 0;
		}
	}

	//
	// Check the intersection point is inside the triangle.
	//
	{
		float u1 = b[i0] - a[i0];
		float v1 = b[i1] - a[i1];
		float u2 = c[i0] - a[i0];
		float v2 = c[i1] - a[i1];
		float u0 = t * ray.getDirection()[i0] + ray.getOrigin()[i0] - a[i0];
		float v0 = t * ray.getDirection()[i1] + ray.getOrigin()[i1] - a[i1];

		float alpha = u0 * v2 - u2 * v0;
		float beta  = u1 * v0 - u0 * v1;
		float area  = u1 * v2 - u2 * v1;

		// epsilon to avoid float precision error
		const float EPSILON = 1e-6f;

		float tolerance = - EPSILON * area;

		if (area > 0)
		{
			if (alpha < tolerance || beta < tolerance || alpha+beta > area-tolerance)
				return std::pair<bool, float>(false, 0);
		}
		else
		{
			if (alpha > tolerance || beta > tolerance || alpha+beta < area-tolerance)
				return std::pair<bool, float>(false, 0);
		}
	}

	return std::pair<bool, float>(true, t);
}
//-----------------------------------------------------------------------
std::pair<bool, float> Math::intersects(const Ray& ray, const Vector3& a,
	const Vector3& b, const Vector3& c,
	bool positiveSide, bool negativeSide)
{
	Vector3 normal = calculateBasicFaceNormalWithoutNormalize(a, b, c);
	return intersects(ray, a, b, c, normal, positiveSide, negativeSide);
}
//-----------------------------------------------------------------------
bool Math::intersects(const Sphere& sphere, const AxisAlignedBox& box)
{
	if (box.isNull()) return false;
	if (box.isInfinite()) return true;

	// Use splitting planes
	const Vector3& center = sphere.getCenter();
	float radius = sphere.getRadius();
	const Vector3& min = box.getMinimum();
	const Vector3& max = box.getMaximum();

	// Arvo's algorithm
	float s, d = 0;
	for (int i = 0; i < 3; ++i)
	{
		if (center.ptr()[i] < min.ptr()[i])
		{
			s = center.ptr()[i] - min.ptr()[i];
			d += s * s; 
		}
		else if(center.ptr()[i] > max.ptr()[i])
		{
			s = center.ptr()[i] - max.ptr()[i];
			d += s * s; 
		}
	}
	return d <= radius * radius;

}
//-----------------------------------------------------------------------
bool Math::intersects(const Plane& plane, const AxisAlignedBox& box)
{
	return (plane.getSide(box) == Plane::BOTH_SIDE);
}
//-----------------------------------------------------------------------
bool Math::intersects(const Sphere& sphere, const Plane& plane)
{
	return (
		Math::Abs(plane.getDistance(sphere.getCenter()))
		<= sphere.getRadius() );
}
//-----------------------------------------------------------------------
Vector3 Math::calculateTangentSpaceVector(
	const Vector3& position1, const Vector3& position2, const Vector3& position3,
	float u1, float v1, float u2, float v2, float u3, float v3)
{
	//side0 is the vector along one side of the triangle of vertices passed in, 
	//and side1 is the vector along another side. Taking the cross product of these returns the normal.
	Vector3 side0 = position1 - position2;
	Vector3 side1 = position3 - position1;
	//Calculate face normal
	Vector3 normal = side1.crossProduct(side0);
	normal.normalise();
	//Now we use a formula to calculate the tangent. 
	float deltaV0 = v1 - v2;
	float deltaV1 = v3 - v1;
	Vector3 tangent = deltaV1 * side0 - deltaV0 * side1;
	tangent.normalise();
	//Calculate binormal
	float deltaU0 = u1 - u2;
	float deltaU1 = u3 - u1;
	Vector3 binormal = deltaU1 * side0 - deltaU0 * side1;
	binormal.normalise();
	//Now, we take the cross product of the tangents to get a vector which 
	//should point in the same direction as our normal calculated above. 
	//If it points in the opposite direction (the dot product between the normals is less than zero), 
	//then we need to reverse the s and t tangents. 
	//This is because the triangle has been mirrored when going from tangent space to object space.
	//reverse tangents if necessary
	Vector3 tangentCross = tangent.crossProduct(binormal);
	if (tangentCross.dotProduct(normal) < 0.0f)
	{
		tangent = -tangent;
		binormal = -binormal;
	}

	return tangent;

}
//-----------------------------------------------------------------------
Matrix4 Math::buildReflectionMatrix(const Plane& p)
{
	return Matrix4(
		-2 * p.normal.x * p.normal.x + 1,   -2 * p.normal.x * p.normal.y,       -2 * p.normal.x * p.normal.z,       -2 * p.normal.x * p.d, 
		-2 * p.normal.y * p.normal.x,       -2 * p.normal.y * p.normal.y + 1,   -2 * p.normal.y * p.normal.z,       -2 * p.normal.y * p.d, 
		-2 * p.normal.z * p.normal.x,       -2 * p.normal.z * p.normal.y,       -2 * p.normal.z * p.normal.z + 1,   -2 * p.normal.z * p.d, 
		0,                                  0,                                  0,                                  1);
}
//-----------------------------------------------------------------------
Vector4 Math::calculateFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3)
{
	Vector3 normal = calculateBasicFaceNormal(v1, v2, v3);
	// Now set up the w (distance of tri from origin
	return Vector4(normal.x, normal.y, normal.z, -(normal.dotProduct(v1)));
}
//-----------------------------------------------------------------------
Vector3 Math::calculateBasicFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3)
{
	Vector3 normal = (v2 - v1).crossProduct(v3 - v1);
	normal.normalise();
	return normal;
}
//-----------------------------------------------------------------------
Vector4 Math::calculateFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3)
{
	Vector3 normal = calculateBasicFaceNormalWithoutNormalize(v1, v2, v3);
	// Now set up the w (distance of tri from origin)
	return Vector4(normal.x, normal.y, normal.z, -(normal.dotProduct(v1)));
}
//-----------------------------------------------------------------------
Vector3 Math::calculateBasicFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3)
{
	Vector3 normal = (v2 - v1).crossProduct(v3 - v1);
	return normal;
}
//-----------------------------------------------------------------------
float Math::gaussianDistribution(float x, float offset, float scale)
{
	float nom = Math::Exp(
		-Math::Sqr(x - offset) / (2 * Math::Sqr(scale)));
	float denom = scale * Math::Sqrt(2 * Math::PI);

	return nom / denom;

}
//---------------------------------------------------------------------
Matrix4 Math::makeViewMatrix(const Vector3& position, const Quaternion& orientation, 
	const Matrix4* reflectMatrix)
{
	Matrix4 viewMatrix;

	// View matrix is:
	//
	//  [ Lx  Uy  Dz  Tx  ]
	//  [ Lx  Uy  Dz  Ty  ]
	//  [ Lx  Uy  Dz  Tz  ]
	//  [ 0   0   0   1   ]
	//
	// Where T = -(Transposed(Rot) * Pos)

	// This is most efficiently done using 3x3 Matrices
	Matrix3 rot;
	orientation.ToRotationMatrix(rot);

	// Make the translation relative to new axes
	Matrix3 rotT = rot.Transpose();
	Vector3 trans = -rotT * position;

	// Make final matrix
	viewMatrix = Matrix4::IDENTITY;
	viewMatrix = rotT; // fills upper 3x3
	viewMatrix[0][3] = trans.x;
	viewMatrix[1][3] = trans.y;
	viewMatrix[2][3] = trans.z;

	// Deal with reflections
	if (reflectMatrix)
	{
		viewMatrix = viewMatrix * (*reflectMatrix);
	}

	return viewMatrix;

}
//---------------------------------------------------------------------
float Math::boundingRadiusFromAABB(const AxisAlignedBox& aabb)
{
	Vector3 max = aabb.getMaximum();
	Vector3 min = aabb.getMinimum();

	Vector3 magnitude = max;
	magnitude.makeCeil(-max);
	magnitude.makeCeil(min);
	magnitude.makeCeil(-min);

	return magnitude.length();
}
